Right, I've been keeping an eye on this one for a while and I'm rather glad no one has attempted to answer it.

This is an interesting question but far, far too broad. Firstly, there is the matter of period (c.500-1500) and geography (you don't actually define Europe, although that's the place most commonly associated with 'medieval'): when/where. While the relationships themselves might not have been substantially different the ability of historians to determine this may well have. For example, there are vast swathes of history where the chief form of evidence is archaeological with some smatterings of contemporary (albeit probably copied in later manuscripts) annals or chronicles. This is true of much of Western Europe up to the Carolingian period, and Eastern and Central Europe up to approaching 1300. Archaeological evidence is, by its nature, circumstantial. We cannot create narratives or extrapolate easily for scenarios we do not have readily available evidence for. So if our chief source of evidence is burials, for example, it is rather more difficult to ascertain what day-to-day life might have been like or how social or political bonds were formed. Likewise, although it is somewhat more usable, annal and chronicle records do not usually deal with the more mundane aspects of life. So we might learn about how one lord expressed his amicable relations with another lord but we're much less likely to have surviving records of how townspeople or villages dealt with one another.

Northern Europe, such as Scandinavia, becomes a much more accessible topic in terms of sources due to the sagas as repositories of social and political networks, although somewhat abstracted, as they deal so heavily with feuds.

All of this evidence is, however, weighted by social standing. The most powerful and influential were considered worth keeping track of and as a result many of the lower classes are lost between the cracks of historical providence. This is an important idea to bear in mind when formulating your future questions (who).

As we approach the Central (or High) Middle Ages (c.950-c.1320) there is a gradual shift from oral to documentary record keeping, which in England are an especially rich resource for uncovering the conflicts and agreements of non-elite, and more exhaustive legal codes reveal the expectations of jurists and lawyers regarding socio-political networks.

Another key development is the great survival of vernacular literary traditions, which can range in content but were still largely the preserve of the social elite. The gap is, however, broadening and we can begin to uncover much more information about the 'middling' class between the aristocracy and the non-martial but 'free' persons who might not yet claim to be aristocrats. Slaves, serfs, and peasants, remain a somewhat muted voice in vernacular traditions into the thirteenth-century but as we move into the fourteenth-century things begin to change. Where voices do emerge they tend to be in rather exceptional circumstances, such as the Inquisitional records of southern France.

In fact, it begins to change rather dramatically. The Black Death created a vastly different economic and social outlook to the thirteenth-century, for the laboratores at least. This has been frequently described as the 'golden age' of the peasant worker. Movement became much easier, wages generally rose (even for women, who could now demand a near parity with male harvesters). Greater literacy and flourishing vernacular traditions gave birth to some of the finest resources for understanding interpersonal relationships (such as Chaucer's Canterbury Tales, The Book of Margery Kempe, Piers Plowman, Gawain and the Greene Knight, to name a few insular examples from across the socio-political divide). This is in addition to the excellent legal records. Moving swiftly into the fifteenth-century the picture is generally much clearer across the board. All of the innovations of the previous few centuries have remained in tact, there is a greater diversity and number of surviving sources and the picture can be much more accurately established.

It is not unlikely that a historian of any period with some reasonable knowledge of the core sources will be able to reconstruct some of the socio-political interpersonal relationships you are asking about (especially in the negative - who was fighting who and how - as this kind of stuff leaves a mark on a wider community than friendship does, at least in terms of surviving record).

So that should help with when/where/who, although note that I am largely discussing England. As this is an Anglophone community there are more specialists concerned with, or at least able to find specialist literature concerned with, England in the Middle Ages. Others with more specialised knowledge of Hungary, Poland, or Scandinavia might disagree with my comments based on their more specialised knowledge of their particular sources.

We move onto the final point, which is slightly more difficult for me to gauge and express in a way that doesn't seem, well, condescending.

This is why. Why are you interested in personal/social relationships? I don't think any historian will be able to quantify how many friends a person might have had (we don't have Facebook lists, flawed though those are); nor have you particularly expressed what you mean by 'how close could they be'. You're next question is answerable, but not many people are actually going to go into it, because you leave it so open-ended. 'What would happen' - what does this mean?

You are asking a question, you are expecting some form of answer. People will be more inclined to answer if they think you're actually interested in the topic rather than it has popped into your head and will likely be gone within the week; and you will get a more detailed response attuned to your interests if you put the effort into going through the when/where/who/why process before posting. This does not mean you have to say, 'I want to know how a Yorkshire miller in 1125 would deal with one of his best friends sleeping with his wife' (this is too specific), but if you could narrow it down to a certain social class, a certain geographical region, and explain a particular facet of socio-political bonds, then you will likely receive an answer providing someone has the specialism and time to draft one. This might mean having a look through the list of flares and PMing someone with relevant expertise, or it might mean picking up an overview book (or using Wikipedia) to narrow your question.